We study the topological properties of elementary excitations in a staggered px±ipy Bose-Einstein condensate realized in recent orbital optical lattice experiments. The condensate wave function may be viewed as a configuration space variant of the famous px+ipy momentum space order parameter of strontium ruthenate superconductors. We show that its elementary excitation spectrum possesses Dirac bosons with π Berry flux. Remarkably, if we induce a population imbalance between the px+ipy and px−ipy condensate components, a gap opens up in the excitation spectrum resulting in a nonzero Chern invariant and topologically protected edge excitation modes. We give a detailed description of how our proposal can be implemented with standard experimental technology.